Ask Question
15 January, 05:56

A hollow aluminum cylinder 19.0 cm deep has an internal capacity of 2.000 L at 23.0°C. It is completely filled with turpentine at 23.0°C. The turpentine and the aluminum cylinder are then slowly warmed together to 91.0°C. (The average linear expansion coefficient for aluminum is 2.4 x10^-5/°C, and the average volume expansion coefficient for turpentine is 9.0 x10^-4/°C.)

(a) How much turpentine overflows?

in cm^3?

(b) What is the volume of turpentine remaining in the cylinder at 91.0°C? (Give you answer to four significant figures.)

in cm^3?

(c) If the combination with this amount of turpentine is then cooled back to 23.0°C, how far below the cylinder's rim does the turpentine's surface recede?

in cm?

+3
Answers (1)
  1. 15 January, 07:35
    0
    (a) 0.1134 L

    (b) 2.009 L

    (c) 0.07 cm from the top

    Explanation:

    The volume of the aluminum container and the turpentine is 2.000 L at 23 °C.

    (a) When the entire system is heated to from 23 °C to 91 °C. The volume of the aluminum container is:

    Vf = Vi * (1 + 3α*ΔT)

    where:

    Vi is the initial volume, Vf the final volume, α is the linear expansion coefficient and ΔT is the temperature change.

    Vf = 2*[1 + 3*2.4 * 10^-5 * (91 - 23) ] = 2.009 L

    The volume of the turpentine is

    Vf = Vi * (1 + β*ΔT)

    where:

    β is the volume expansion coefficient

    Vf = 2*[1 + 9.0*10^-4 * (91 - 23) ] = 2.1224 L

    The overflow is:

    2.1224 - 2.009 = 0.1134 L

    (b) the volume of turpentine remaining in the cylinder at 91 °C is the same volume of the hollow aluminum cylinder, that is, 2.009 L

    (c) Cooling the system back to 23 °C means the aluminum container is back to 2.000 L. The volume of turpentine is:

    Vf = 2.1224*[1 + 9.0*10^-4 * (23-91) ] = 1.9925 L

    The following proportion must be satisfied:

    Volume of turpentine / Volume of container = deep turpentine / deep of container

    1.9925 / 2.000 = deep turpentine/19

    deep turpentine = (1.9925 / 2.000) * 19 = 18.93 cm

    This is 19 - 18.93 = 0.07 cm from the top
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A hollow aluminum cylinder 19.0 cm deep has an internal capacity of 2.000 L at 23.0°C. It is completely filled with turpentine at 23.0°C. ...” in 📙 Physics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers